Shadowheart does seem to be the most tied into the story so far, with the box and the Sharran/Selunite connections in act 1. And Shadowheart is really versatile and can take care of any lockpicking/stealth/disarming, can buff, heal, do okay damage and be more tanky if specced that way. Basically, she frees you up to take whatever other party members and play whatever PC you want.
Wyll has more stuff going on with the goblins, true, and Lae’zel with the gith patrol, though if following Lae’zel you’d probably fairly quickly head off to the mountain pass towards the crèche rather than going via the Underdark or even bothering with the goblin camp, so lore wise she will probably make more sense in the full release when we can follow that lead. Astarion just has the interaction with Gandrel, I think plus interest in the Necromancy of Thay. Gale just has the Necromancy of Thay, plus chance of dying to get some insight into his condition if he travels with you and interjections in the druid camp that give some details of his past in Waterdeep.
Which is a long way of saying that I agree Shadowheart and Wyll probably have the most story in EA, with specific bits that it’s worth having Lae’zel and Astarion for, but those are signalled well enough in-game to make it not metagaming to just swap them in when relevant, keeping a free party slot for whoever. For Tav, there’s probably most resonance for tiefling, drow or deep gnome races and perhaps druid as a class, but it’s all pretty open at this stage.
